Investment Function

“By investment
is meant an addition of capital such as occurs when a new house is built or a new factory
is built. Investment means making an addition to the stock of goods in existence.”

The Decision to Invest

The decision to invest is different as compared to the decision to buy consumer goods.
This is due to the following reasons:

A firm must make a decision whether to go for capital expansion or buy an existing
asset like equity in another company.

Most of the Capital goods have a long life and one can only several years later
as to whether the investment in these capital goods has been profitable or not.

When a firm has decided to expand it will have to decide as to whether the cost
of borrowing in greater than the return expected on the new investment undertaken
by the firm.

A firm investment decision is based on the relationship between three elements:

Expected income flow from capital good under consideration: As the future is uncertain
a crucial decision of the firm in making its investment decision is regarding two
aspects:

An estimate of the future flow of income that the capital asset under consideration
is expected to yield over its entire life.

The expected life of the capital good which may last more than expected or
may become obsolete before its lifetime due to technological advancements.

The purchase price of the good in question: Often there exists an uncertainty regarding
the price at which the good is to be purchased. This is more for projects where
new machines and equipment are involved and where the cost may undergo change over
time.

The rate of interest prevailing in the market which again is subject to fluctuations.
It is important to note that any calculations that relate to the future must take
into consideration the fact that the returns over the future have a much lower
worth as compared to the same returns today.

While making an investment decision relating to future, a calculation may be made
regarding the present value of the capital asset and the discounted rate of return
on the asset.

Let us see few illustrations which explain various models of investment.

Illustration 26

Presume that $ 200 is to be received by an individual after a period of 1 year. The
market rate of interest is 20 %. How much must he invest today?

Solution

The discounted present value of $ 200 is

Ro = 200
(1+0.20)

= 166.67

This implies that to get a sum of $200 at the end of 1 year is $166.67 must
be invested today at an interest of 20% pa.

Equation (2) can be written as

Ro = Rn
(1+r)^n

Where (1+r) = discount
rate

Rn = the
discounted present value of Rn
(1+r)^n

We consider the determination of the present value of a bond. Bonds yields a yearly
income, say R, until it reaches maturity at the end of n years when it returns the
principle amount, P the present value of the bond is

V = R + R + R +….+ R + P
(1+r) (1+r)^2 (1+r)^3 (1+r)^n (1+r)^n

Alternatively, a machine is expected to yield an income stream of R1, R2, R3 to Rn over
a period of its entire life. At the end, it has a scrap value of J. The market rate
of interest is r. the present value of the returns from the machine is

V = R1 + R2 + R3 +….+ Rn + J
(1+r) (1+r)^2 (1+r)^3 (1+r)^n (1+r)^n

Illustration 27

Suppose the annual expected returns from a machine are $70 thousands over a period of years,
which is the expected economic life of the machine. The scrap value of the machine
is $ 40 thousands.

The market rate of interest is 20 %. The cost of the machine is $ 150,000. Find the
present value of expected returns from the machine. Is it able to invest in the machine.

As the discounted present value of the returns from the machine is $197,297,
which is greater than the cost of the machine, $ 150,000 the investment in the
machine is profitable.

Illustration 28

In the event, if it costs $ 6,000 to invest in a certain machinery and the life of the
machinery is two years that is after two years it becomes quite useless having no value.

Presume further that in the first year of machinery is expected to yield income of $
2,200 and in the second year $ 4,840.

Solution

By substituting these values in the above formula, we can calculate the value of r,
which is the marginal efficiency of capital.

C = R1 + R2
(1
+ r) (1
+ r)^2

6,000 = 2,200 + 4,840
(1+r) (1+r)^2

On calculating the value of r in the above equation it is found to be equal to 10. In
other words, marginal efficiency of capital is here equal to 10 %. If we put the value
of r, that is 10 in the above equation, we obtain the following:

6,000 = 2,200 + 4,840
1.10 (1.10)^2
6,000 = 2,000 + 4,000

6,000 = 6,000

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